From 85e509d2026040d0b51835850b7279d745f83f7c Mon Sep 17 00:00:00 2001
From: Gautam Botrel <gautam.botrel@gmail.com>
Date: Sat, 28 Sep 2024 15:18:12 +0000
Subject: [PATCH] feat: update bavard and use better syntax in asm

---
 ecc/bls12-377/fp/element_ops_amd64.s          |   2 +-
 ecc/bls12-377/fp/vector_test.go               |   4 +-
 ecc/bls12-377/fr/element_ops_amd64.go         |  10 +-
 ecc/bls12-377/fr/element_ops_amd64.s          |   4 +-
 ecc/bls12-377/fr/vector_test.go               |   4 +-
 ecc/bls12-381/fp/element_ops_amd64.s          |   2 +-
 ecc/bls12-381/fp/vector_test.go               |   4 +-
 ecc/bls12-381/fr/element_ops_amd64.go         |  10 +-
 ecc/bls12-381/fr/element_ops_amd64.s          |   4 +-
 ecc/bls12-381/fr/vector_test.go               |   4 +-
 ecc/bls24-315/fp/element_ops_amd64.s          |   2 +-
 ecc/bls24-315/fp/vector_test.go               |   4 +-
 ecc/bls24-315/fr/element_ops_amd64.go         |  10 +-
 ecc/bls24-315/fr/element_ops_amd64.s          |   4 +-
 ecc/bls24-315/fr/vector_test.go               |   4 +-
 ecc/bls24-317/fp/element_ops_amd64.s          |   2 +-
 ecc/bls24-317/fp/vector_test.go               |   4 +-
 ecc/bls24-317/fr/element_ops_amd64.go         |  10 +-
 ecc/bls24-317/fr/element_ops_amd64.s          |   4 +-
 ecc/bls24-317/fr/vector_test.go               |   4 +-
 ecc/bn254/fp/element_ops_amd64.go             |  10 +-
 ecc/bn254/fp/element_ops_amd64.s              |   4 +-
 ecc/bn254/fp/vector_test.go                   |   4 +-
 ecc/bn254/fr/element_ops_amd64.go             |  10 +-
 ecc/bn254/fr/element_ops_amd64.s              |   4 +-
 ecc/bn254/fr/vector_test.go                   |   4 +-
 ecc/bw6-633/fp/element_ops_amd64.s            |   2 +-
 ecc/bw6-633/fp/vector_test.go                 |   4 +-
 ecc/bw6-633/fr/element_ops_amd64.s            |   2 +-
 ecc/bw6-633/fr/vector_test.go                 |   4 +-
 ecc/bw6-761/fp/element_ops_amd64.s            |   2 +-
 ecc/bw6-761/fp/vector_test.go                 |   4 +-
 ecc/bw6-761/fr/element_ops_amd64.s            |   2 +-
 ecc/bw6-761/fr/vector_test.go                 |   4 +-
 ecc/secp256k1/fp/vector_test.go               |   4 +-
 ecc/secp256k1/fr/vector_test.go               |   4 +-
 ecc/stark-curve/fp/element_ops_amd64.go       |  10 +-
 ecc/stark-curve/fp/element_ops_amd64.s        |   4 +-
 ecc/stark-curve/fp/vector_test.go             |   4 +-
 ecc/stark-curve/fr/element_ops_amd64.go       |  10 +-
 ecc/stark-curve/fr/element_ops_amd64.s        |   4 +-
 ecc/stark-curve/fr/vector_test.go             |   4 +-
 field/asm/element_10w_amd64.s                 |  15 +-
 field/asm/element_12w_amd64.s                 |  15 +-
 field/asm/element_4w_amd64.s                  |  15 +-
 field/asm/element_5w_amd64.s                  |  15 +-
 field/asm/element_6w_amd64.s                  |  15 +-
 field/asm/vector_4w_amd64.s                   | 550 ++++++++----------
 field/generator/asm/amd64/build.go            |  36 +-
 field/generator/asm/amd64/element_mul.go      |   1 +
 field/generator/asm/amd64/element_vec.go      | 339 ++---------
 .../internal/templates/element/ops_asm.go     |  10 +-
 .../templates/element/tests_vector.go         |   4 +-
 field/goldilocks/vector_test.go               |   4 +-
 go.mod                                        |   4 +-
 go.sum                                        |   4 +-
 56 files changed, 442 insertions(+), 785 deletions(-)

diff --git a/ecc/bls12-377/fp/element_ops_amd64.s b/ecc/bls12-377/fp/element_ops_amd64.s
index ec133ebb5..7d569a34f 100644
--- a/ecc/bls12-377/fp/element_ops_amd64.s
+++ b/ecc/bls12-377/fp/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 4744144000832074674
+// We include the hash to force the Go compiler to recompile: 9834095789769468746
 #include "../../../field/asm/element_6w_amd64.s"
 
diff --git a/ecc/bls12-377/fp/vector_test.go b/ecc/bls12-377/fp/vector_test.go
index 5c4e3a6c3..bdce3116b 100644
--- a/ecc/bls12-377/fp/vector_test.go
+++ b/ecc/bls12-377/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls12-377/fr/element_ops_amd64.go b/ecc/bls12-377/fr/element_ops_amd64.go
index e79066cd4..b0f74525c 100644
--- a/ecc/bls12-377/fr/element_ops_amd64.go
+++ b/ecc/bls12-377/fr/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/bls12-377/fr/element_ops_amd64.s b/ecc/bls12-377/fr/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/bls12-377/fr/element_ops_amd64.s
+++ b/ecc/bls12-377/fr/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/bls12-377/fr/vector_test.go b/ecc/bls12-377/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/bls12-377/fr/vector_test.go
+++ b/ecc/bls12-377/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls12-381/fp/element_ops_amd64.s b/ecc/bls12-381/fp/element_ops_amd64.s
index ec133ebb5..7d569a34f 100644
--- a/ecc/bls12-381/fp/element_ops_amd64.s
+++ b/ecc/bls12-381/fp/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 4744144000832074674
+// We include the hash to force the Go compiler to recompile: 9834095789769468746
 #include "../../../field/asm/element_6w_amd64.s"
 
diff --git a/ecc/bls12-381/fp/vector_test.go b/ecc/bls12-381/fp/vector_test.go
index 5c4e3a6c3..bdce3116b 100644
--- a/ecc/bls12-381/fp/vector_test.go
+++ b/ecc/bls12-381/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls12-381/fr/element_ops_amd64.go b/ecc/bls12-381/fr/element_ops_amd64.go
index e79066cd4..b0f74525c 100644
--- a/ecc/bls12-381/fr/element_ops_amd64.go
+++ b/ecc/bls12-381/fr/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/bls12-381/fr/element_ops_amd64.s b/ecc/bls12-381/fr/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/bls12-381/fr/element_ops_amd64.s
+++ b/ecc/bls12-381/fr/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/bls12-381/fr/vector_test.go b/ecc/bls12-381/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/bls12-381/fr/vector_test.go
+++ b/ecc/bls12-381/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls24-315/fp/element_ops_amd64.s b/ecc/bls24-315/fp/element_ops_amd64.s
index 605f1ee09..5cda5d1b3 100644
--- a/ecc/bls24-315/fp/element_ops_amd64.s
+++ b/ecc/bls24-315/fp/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7085443902529260581
+// We include the hash to force the Go compiler to recompile: 14698325647798323165
 #include "../../../field/asm/element_5w_amd64.s"
 
diff --git a/ecc/bls24-315/fp/vector_test.go b/ecc/bls24-315/fp/vector_test.go
index 6236eafee..5707a6271 100644
--- a/ecc/bls24-315/fp/vector_test.go
+++ b/ecc/bls24-315/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls24-315/fr/element_ops_amd64.go b/ecc/bls24-315/fr/element_ops_amd64.go
index e79066cd4..b0f74525c 100644
--- a/ecc/bls24-315/fr/element_ops_amd64.go
+++ b/ecc/bls24-315/fr/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/bls24-315/fr/element_ops_amd64.s b/ecc/bls24-315/fr/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/bls24-315/fr/element_ops_amd64.s
+++ b/ecc/bls24-315/fr/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/bls24-315/fr/vector_test.go b/ecc/bls24-315/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/bls24-315/fr/vector_test.go
+++ b/ecc/bls24-315/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls24-317/fp/element_ops_amd64.s b/ecc/bls24-317/fp/element_ops_amd64.s
index 605f1ee09..5cda5d1b3 100644
--- a/ecc/bls24-317/fp/element_ops_amd64.s
+++ b/ecc/bls24-317/fp/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7085443902529260581
+// We include the hash to force the Go compiler to recompile: 14698325647798323165
 #include "../../../field/asm/element_5w_amd64.s"
 
diff --git a/ecc/bls24-317/fp/vector_test.go b/ecc/bls24-317/fp/vector_test.go
index 6236eafee..5707a6271 100644
--- a/ecc/bls24-317/fp/vector_test.go
+++ b/ecc/bls24-317/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bls24-317/fr/element_ops_amd64.go b/ecc/bls24-317/fr/element_ops_amd64.go
index e79066cd4..b0f74525c 100644
--- a/ecc/bls24-317/fr/element_ops_amd64.go
+++ b/ecc/bls24-317/fr/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/bls24-317/fr/element_ops_amd64.s b/ecc/bls24-317/fr/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/bls24-317/fr/element_ops_amd64.s
+++ b/ecc/bls24-317/fr/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/bls24-317/fr/vector_test.go b/ecc/bls24-317/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/bls24-317/fr/vector_test.go
+++ b/ecc/bls24-317/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bn254/fp/element_ops_amd64.go b/ecc/bn254/fp/element_ops_amd64.go
index 8f909cd0f..3b78cf464 100644
--- a/ecc/bn254/fp/element_ops_amd64.go
+++ b/ecc/bn254/fp/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/bn254/fp/element_ops_amd64.s b/ecc/bn254/fp/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/bn254/fp/element_ops_amd64.s
+++ b/ecc/bn254/fp/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/bn254/fp/vector_test.go b/ecc/bn254/fp/vector_test.go
index 655f88692..e4996e522 100644
--- a/ecc/bn254/fp/vector_test.go
+++ b/ecc/bn254/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bn254/fr/element_ops_amd64.go b/ecc/bn254/fr/element_ops_amd64.go
index e79066cd4..b0f74525c 100644
--- a/ecc/bn254/fr/element_ops_amd64.go
+++ b/ecc/bn254/fr/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/bn254/fr/element_ops_amd64.s b/ecc/bn254/fr/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/bn254/fr/element_ops_amd64.s
+++ b/ecc/bn254/fr/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/bn254/fr/vector_test.go b/ecc/bn254/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/bn254/fr/vector_test.go
+++ b/ecc/bn254/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bw6-633/fp/element_ops_amd64.s b/ecc/bw6-633/fp/element_ops_amd64.s
index 8fecb7e10..3ba7db746 100644
--- a/ecc/bw6-633/fp/element_ops_amd64.s
+++ b/ecc/bw6-633/fp/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 740214979564192701
+// We include the hash to force the Go compiler to recompile: 2301942780660398757
 #include "../../../field/asm/element_10w_amd64.s"
 
diff --git a/ecc/bw6-633/fp/vector_test.go b/ecc/bw6-633/fp/vector_test.go
index c6dd6cfd1..6a86fd362 100644
--- a/ecc/bw6-633/fp/vector_test.go
+++ b/ecc/bw6-633/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bw6-633/fr/element_ops_amd64.s b/ecc/bw6-633/fr/element_ops_amd64.s
index 605f1ee09..5cda5d1b3 100644
--- a/ecc/bw6-633/fr/element_ops_amd64.s
+++ b/ecc/bw6-633/fr/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7085443902529260581
+// We include the hash to force the Go compiler to recompile: 14698325647798323165
 #include "../../../field/asm/element_5w_amd64.s"
 
diff --git a/ecc/bw6-633/fr/vector_test.go b/ecc/bw6-633/fr/vector_test.go
index 415a8b490..fbea4a859 100644
--- a/ecc/bw6-633/fr/vector_test.go
+++ b/ecc/bw6-633/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bw6-761/fp/element_ops_amd64.s b/ecc/bw6-761/fp/element_ops_amd64.s
index 520b1fb87..53ef94eec 100644
--- a/ecc/bw6-761/fp/element_ops_amd64.s
+++ b/ecc/bw6-761/fp/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 11568055404266003096
+// We include the hash to force the Go compiler to recompile: 15402800788770244368
 #include "../../../field/asm/element_12w_amd64.s"
 
diff --git a/ecc/bw6-761/fp/vector_test.go b/ecc/bw6-761/fp/vector_test.go
index 1daa1dca4..fc4837597 100644
--- a/ecc/bw6-761/fp/vector_test.go
+++ b/ecc/bw6-761/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/bw6-761/fr/element_ops_amd64.s b/ecc/bw6-761/fr/element_ops_amd64.s
index ec133ebb5..7d569a34f 100644
--- a/ecc/bw6-761/fr/element_ops_amd64.s
+++ b/ecc/bw6-761/fr/element_ops_amd64.s
@@ -1,6 +1,6 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 4744144000832074674
+// We include the hash to force the Go compiler to recompile: 9834095789769468746
 #include "../../../field/asm/element_6w_amd64.s"
 
diff --git a/ecc/bw6-761/fr/vector_test.go b/ecc/bw6-761/fr/vector_test.go
index 0cf7bb0b9..02e50c43e 100644
--- a/ecc/bw6-761/fr/vector_test.go
+++ b/ecc/bw6-761/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/secp256k1/fp/vector_test.go b/ecc/secp256k1/fp/vector_test.go
index 655f88692..e4996e522 100644
--- a/ecc/secp256k1/fp/vector_test.go
+++ b/ecc/secp256k1/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/secp256k1/fr/vector_test.go b/ecc/secp256k1/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/secp256k1/fr/vector_test.go
+++ b/ecc/secp256k1/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/stark-curve/fp/element_ops_amd64.go b/ecc/stark-curve/fp/element_ops_amd64.go
index 8f909cd0f..3b78cf464 100644
--- a/ecc/stark-curve/fp/element_ops_amd64.go
+++ b/ecc/stark-curve/fp/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/stark-curve/fp/element_ops_amd64.s b/ecc/stark-curve/fp/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/stark-curve/fp/element_ops_amd64.s
+++ b/ecc/stark-curve/fp/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/stark-curve/fp/vector_test.go b/ecc/stark-curve/fp/vector_test.go
index 655f88692..e4996e522 100644
--- a/ecc/stark-curve/fp/vector_test.go
+++ b/ecc/stark-curve/fp/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/ecc/stark-curve/fr/element_ops_amd64.go b/ecc/stark-curve/fr/element_ops_amd64.go
index e79066cd4..b0f74525c 100644
--- a/ecc/stark-curve/fr/element_ops_amd64.go
+++ b/ecc/stark-curve/fr/element_ops_amd64.go
@@ -101,9 +101,6 @@ func (vector *Vector) Sum() (res Element) {
 //go:noescape
 func sumVec(res *Element, a *Element, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a, b *Element, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res Element) {
@@ -114,10 +111,10 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -126,6 +123,9 @@ func (vector *Vector) InnerProduct(other Vector) (res Element) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a, b *Element, n uint64)
+
 // Mul z = x * y (mod q)
 //
 // x and y must be less than q
diff --git a/ecc/stark-curve/fr/element_ops_amd64.s b/ecc/stark-curve/fr/element_ops_amd64.s
index 3ef8676bb..f547f8246 100644
--- a/ecc/stark-curve/fr/element_ops_amd64.s
+++ b/ecc/stark-curve/fr/element_ops_amd64.s
@@ -1,10 +1,10 @@
 // +build !purego
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 444291736743577851
+// We include the hash to force the Go compiler to recompile: 13361353926491767027
 #include "../../../field/asm/element_4w_amd64.s"
 
 // Code generated by gnark-crypto/generator. DO NOT EDIT.
-// We include the hash to force the Go compiler to recompile: 7023651991118674373
+// We include the hash to force the Go compiler to recompile: 5868826605799376126
 #include "../../../field/asm/vector_4w_amd64.s"
 
diff --git a/ecc/stark-curve/fr/vector_test.go b/ecc/stark-curve/fr/vector_test.go
index f230cab99..6d032b9bd 100644
--- a/ecc/stark-curve/fr/vector_test.go
+++ b/ecc/stark-curve/fr/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/field/asm/element_10w_amd64.s b/field/asm/element_10w_amd64.s
index 9c1f5fe9b..f12cc2ccd 100644
--- a/field/asm/element_10w_amd64.s
+++ b/field/asm/element_10w_amd64.s
@@ -1,17 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
 #include "textflag.h"
 #include "funcdata.h"
 #include "go_asm.h"
diff --git a/field/asm/element_12w_amd64.s b/field/asm/element_12w_amd64.s
index 1a0e759cc..649f94f4b 100644
--- a/field/asm/element_12w_amd64.s
+++ b/field/asm/element_12w_amd64.s
@@ -1,17 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
 #include "textflag.h"
 #include "funcdata.h"
 #include "go_asm.h"
diff --git a/field/asm/element_4w_amd64.s b/field/asm/element_4w_amd64.s
index c2b0fb6cd..cdd59505b 100644
--- a/field/asm/element_4w_amd64.s
+++ b/field/asm/element_4w_amd64.s
@@ -1,17 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
 #include "textflag.h"
 #include "funcdata.h"
 #include "go_asm.h"
diff --git a/field/asm/element_5w_amd64.s b/field/asm/element_5w_amd64.s
index 00065313d..efe7dd0b2 100644
--- a/field/asm/element_5w_amd64.s
+++ b/field/asm/element_5w_amd64.s
@@ -1,17 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
 #include "textflag.h"
 #include "funcdata.h"
 #include "go_asm.h"
diff --git a/field/asm/element_6w_amd64.s b/field/asm/element_6w_amd64.s
index abbbd289b..9cc921008 100644
--- a/field/asm/element_6w_amd64.s
+++ b/field/asm/element_6w_amd64.s
@@ -1,17 +1,4 @@
-// Copyright 2020 ConsenSys Software Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
 #include "textflag.h"
 #include "funcdata.h"
 #include "go_asm.h"
diff --git a/field/asm/vector_4w_amd64.s b/field/asm/vector_4w_amd64.s
index b97a1cf55..16c877490 100644
--- a/field/asm/vector_4w_amd64.s
+++ b/field/asm/vector_4w_amd64.s
@@ -1,3 +1,6 @@
+// Code generated by gnark-crypto/generator. DO NOT EDIT.
+// Functions are derived from Dag Arne Osvik's work in github.com/a16z/vectorized-fields
+
 // addVec(res, a, b *Element, n uint64) res[0...n] = a[0...n] + b[0...n]
 TEXT ·addVec(SB), NOSPLIT, $0-32
 	MOVQ res+0(FP), CX
@@ -517,11 +520,11 @@ accumulate_11:
 	// lo(hi(w1)) -> CX
 	// lo(hi(w2)) -> R15
 	// lo(hi(w3)) -> R14
-#define SPLIT_LO_HI(lo, hi) \
-	MOVQ hi, lo;          \
-	ANDQ $0xffffffff, lo; \
-	SHLQ $32, lo;         \
-	SHRQ $32, hi;         \
+#define SPLIT_LO_HI(in0, in1) \
+	MOVQ in1, in0         \
+	ANDQ $0xffffffff, in0 \
+	SHLQ $32, in0         \
+	SHRQ $32, in1         \
 
 	SPLIT_LO_HI(R13, SI)
 	SPLIT_LO_HI(CX, R8)
@@ -607,9 +610,11 @@ done_9:
 
 // innerProdVec(res, a,b *Element, n uint64) res = sum(a[0...n] * b[0...n])
 TEXT ·innerProdVec(SB), NOSPLIT, $0-32
-	MOVQ      a+8(FP), R14
-	MOVQ      b+16(FP), R15
-	MOVQ      n+24(FP), CX
+	MOVQ a+8(FP), R14
+	MOVQ b+16(FP), R15
+	MOVQ n+24(FP), CX
+
+	// Create mask for low dword in each qword
 	VPCMPEQB  Y0, Y0, Y0
 	VPMOVZXDQ Y0, Z5
 	VPXORQ    Z16, Z16, Z16
@@ -638,327 +643,238 @@ loop_13:
 	ADDQ      $32, R15
 
 	// we multiply and accumulate partial products of 4 bytes * 32 bytes
-	VPMULUDQ.BCST 0*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z16, Z16
-	VPADDQ        Z3, Z24, Z24
-	VPMULUDQ.BCST 1*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z17, Z17
-	VPADDQ        Z3, Z25, Z25
-	VPMULUDQ.BCST 2*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z18, Z18
-	VPADDQ        Z3, Z26, Z26
-	VPMULUDQ.BCST 3*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z19, Z19
-	VPADDQ        Z3, Z27, Z27
-	VPMULUDQ.BCST 4*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z20, Z20
-	VPADDQ        Z3, Z28, Z28
-	VPMULUDQ.BCST 5*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z21, Z21
-	VPADDQ        Z3, Z29, Z29
-	VPMULUDQ.BCST 6*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z22, Z22
-	VPADDQ        Z3, Z30, Z30
-	VPMULUDQ.BCST 7*4(R14), Z4, Z2
-	VPSRLQ        $32, Z2, Z3
-	VPANDQ        Z5, Z2, Z2
-	VPADDQ        Z2, Z23, Z23
-	VPADDQ        Z3, Z31, Z31
-	ADDQ          $32, R14
-	DECQ          CX               // decrement n
-	JMP           loop_13
+#define MAC(in0, in1, in2) \
+	VPMULUDQ.BCST in0, Z4, Z2  \
+	VPSRLQ        $32, Z2, Z3  \
+	VPANDQ        Z5, Z2, Z2   \
+	VPADDQ        Z2, in1, in1 \
+	VPADDQ        Z3, in2, in2 \
+
+	MAC(0*4(R14), Z16, Z24)
+	MAC(1*4(R14), Z17, Z25)
+	MAC(2*4(R14), Z18, Z26)
+	MAC(3*4(R14), Z19, Z27)
+	MAC(4*4(R14), Z20, Z28)
+	MAC(5*4(R14), Z21, Z29)
+	MAC(6*4(R14), Z22, Z30)
+	MAC(7*4(R14), Z23, Z31)
+	ADDQ $32, R14
+	DECQ CX       // decrement n
+	JMP  loop_13
 
 accumulate_15:
+	// we accumulate the partial products into 544bits in Z1:Z0
 	MOVQ  $0x0000000000001555, AX
 	KMOVD AX, K1
 	MOVQ  $1, AX
 	KMOVD AX, K2
 
 	// store the least significant 32 bits of ACC (starts with A0L) in Z0
-	VALIGND.Z   $16, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z24, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z17, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $15, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z24, Z24
-	VPADDQ      Z24, Z16, Z16
-	VPSRLQ      $32, Z17, Z17
-	VPADDQ      Z17, Z16, Z16
-	VPANDQ      Z5, Z25, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z18, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-2, Z16, Z16, K2, Z0
-	KADDW       K2, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z25, Z25
-	VPADDQ      Z25, Z16, Z16
-	VPSRLQ      $32, Z18, Z18
-	VPADDQ      Z18, Z16, Z16
-	VPANDQ      Z5, Z26, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z19, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-3, Z16, Z16, K2, Z0
-	KADDW       K2, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z26, Z26
-	VPADDQ      Z26, Z16, Z16
-	VPSRLQ      $32, Z19, Z19
-	VPADDQ      Z19, Z16, Z16
-	VPANDQ      Z5, Z27, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z20, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-4, Z16, Z16, K2, Z0
-	KADDW       K2, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z27, Z27
-	VPADDQ      Z27, Z16, Z16
-	VPSRLQ      $32, Z20, Z20
-	VPADDQ      Z20, Z16, Z16
-	VPANDQ      Z5, Z28, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z21, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-5, Z16, Z16, K2, Z0
-	KADDW       K2, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z28, Z28
-	VPADDQ      Z28, Z16, Z16
-	VPSRLQ      $32, Z21, Z21
-	VPADDQ      Z21, Z16, Z16
-	VPANDQ      Z5, Z29, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z22, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-6, Z16, Z16, K2, Z0
-	KADDW       K2, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z29, Z29
-	VPADDQ      Z29, Z16, Z16
-	VPSRLQ      $32, Z22, Z22
-	VPADDQ      Z22, Z16, Z16
-	VPANDQ      Z5, Z30, Z2
-	VPADDQ      Z2, Z16, Z16
-	VPANDQ      Z5, Z23, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-7, Z16, Z16, K2, Z0
-	KADDW       K2, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z30, Z30
-	VPADDQ      Z30, Z16, Z16
-	VPSRLQ      $32, Z23, Z23
-	VPADDQ      Z23, Z16, Z16
-	VPANDQ      Z5, Z31, Z2
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-8, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VPSRLQ      $32, Z31, Z31
-	VPADDQ      Z31, Z16, Z16
-	VALIGND     $16-9, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-10, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-11, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-12, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-13, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-14, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
-	VPSRLQ      $32, Z16, Z2
-	VALIGND.Z   $2, Z16, Z16, K1, Z16
-	VPADDQ      Z2, Z16, Z16
-	VALIGND     $16-15, Z16, Z16, K2, Z0
-	KSHIFTLW    $1, K2, K2
+	VALIGND.Z $16, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+	VPSRLQ    $32, Z16, Z2
+	VALIGND.Z $2, Z16, Z16, K1, Z16
+	VPADDQ    Z2, Z16, Z16
+	VPANDQ    Z5, Z24, Z2
+	VPADDQ    Z2, Z16, Z16
+	VPANDQ    Z5, Z17, Z2
+	VPADDQ    Z2, Z16, Z16
+	VALIGND   $15, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+
+	// macro to add partial products and store the result in Z0
+#define ADDPP(in0, in1, in2, in3, in4) \
+	VPSRLQ    $32, Z16, Z2              \
+	VALIGND.Z $2, Z16, Z16, K1, Z16     \
+	VPADDQ    Z2, Z16, Z16              \
+	VPSRLQ    $32, in0, in0             \
+	VPADDQ    in0, Z16, Z16             \
+	VPSRLQ    $32, in1, in1             \
+	VPADDQ    in1, Z16, Z16             \
+	VPANDQ    Z5, in2, Z2               \
+	VPADDQ    Z2, Z16, Z16              \
+	VPANDQ    Z5, in3, Z2               \
+	VPADDQ    Z2, Z16, Z16              \
+	VALIGND   $16-in4, Z16, Z16, K2, Z0 \
+	KADDW     K2, K2, K2                \
+
+	ADDPP(Z24, Z17, Z25, Z18, 2)
+	ADDPP(Z25, Z18, Z26, Z19, 3)
+	ADDPP(Z26, Z19, Z27, Z20, 4)
+	ADDPP(Z27, Z20, Z28, Z21, 5)
+	ADDPP(Z28, Z21, Z29, Z22, 6)
+	ADDPP(Z29, Z22, Z30, Z23, 7)
+	VPSRLQ    $32, Z16, Z2
+	VALIGND.Z $2, Z16, Z16, K1, Z16
+	VPADDQ    Z2, Z16, Z16
+	VPSRLQ    $32, Z30, Z30
+	VPADDQ    Z30, Z16, Z16
+	VPSRLQ    $32, Z23, Z23
+	VPADDQ    Z23, Z16, Z16
+	VPANDQ    Z5, Z31, Z2
+	VPADDQ    Z2, Z16, Z16
+	VALIGND   $16-8, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+	VPSRLQ    $32, Z16, Z2
+	VALIGND.Z $2, Z16, Z16, K1, Z16
+	VPADDQ    Z2, Z16, Z16
+	VPSRLQ    $32, Z31, Z31
+	VPADDQ    Z31, Z16, Z16
+	VALIGND   $16-9, Z16, Z16, K2, Z0
+	KSHIFTLW  $1, K2, K2
+
+#define ADDPP2(in0) \
+	VPSRLQ    $32, Z16, Z2              \
+	VALIGND.Z $2, Z16, Z16, K1, Z16     \
+	VPADDQ    Z2, Z16, Z16              \
+	VALIGND   $16-in0, Z16, Z16, K2, Z0 \
+	KSHIFTLW  $1, K2, K2                \
+
+	ADDPP2(10)
+	ADDPP2(11)
+	ADDPP2(12)
+	ADDPP2(13)
+	ADDPP2(14)
+	ADDPP2(15)
 	VPSRLQ      $32, Z16, Z2
 	VALIGND.Z   $2, Z16, Z16, K1, Z16
 	VPADDQ      Z2, Z16, Z16
 	VMOVDQA64.Z Z16, K1, Z1
-	VMOVQ       X0, SI
-	VALIGNQ     $1, Z0, Z1, Z0
-	VMOVQ       X0, DI
-	VALIGNQ     $1, Z0, Z0, Z0
-	VMOVQ       X0, R8
-	VALIGNQ     $1, Z0, Z0, Z0
-	VMOVQ       X0, R9
-	VALIGNQ     $1, Z0, Z0, Z0
-	XORQ        BX, BX
-	MOVQ        $const_qInvNeg, DX
-	MULXQ       SI, DX, R10
-	MULXQ       ·qElement+0(SB), AX, R10
-	ADDQ        AX, SI
-	ADCQ        R10, DI
-	MULXQ       ·qElement+16(SB), AX, R10
-	ADCQ        AX, R8
-	ADCQ        R10, R9
-	ADCQ        $0, BX
-	MULXQ       ·qElement+8(SB), AX, R10
-	ADDQ        AX, DI
-	ADCQ        R10, R8
-	MULXQ       ·qElement+24(SB), AX, R10
-	ADCQ        AX, R9
-	ADCQ        R10, BX
-	ADCQ        $0, SI
-	MOVQ        $const_qInvNeg, DX
-	MULXQ       DI, DX, R10
-	MULXQ       ·qElement+0(SB), AX, R10
-	ADDQ        AX, DI
-	ADCQ        R10, R8
-	MULXQ       ·qElement+16(SB), AX, R10
-	ADCQ        AX, R9
-	ADCQ        R10, BX
-	ADCQ        $0, SI
-	MULXQ       ·qElement+8(SB), AX, R10
-	ADDQ        AX, R8
-	ADCQ        R10, R9
-	MULXQ       ·qElement+24(SB), AX, R10
-	ADCQ        AX, BX
-	ADCQ        R10, SI
-	ADCQ        $0, DI
-	MOVQ        $const_qInvNeg, DX
-	MULXQ       R8, DX, R10
-	MULXQ       ·qElement+0(SB), AX, R10
-	ADDQ        AX, R8
-	ADCQ        R10, R9
-	MULXQ       ·qElement+16(SB), AX, R10
-	ADCQ        AX, BX
-	ADCQ        R10, SI
-	ADCQ        $0, DI
-	MULXQ       ·qElement+8(SB), AX, R10
-	ADDQ        AX, R9
-	ADCQ        R10, BX
-	MULXQ       ·qElement+24(SB), AX, R10
-	ADCQ        AX, SI
-	ADCQ        R10, DI
-	ADCQ        $0, R8
-	MOVQ        $const_qInvNeg, DX
-	MULXQ       R9, DX, R10
-	MULXQ       ·qElement+0(SB), AX, R10
-	ADDQ        AX, R9
-	ADCQ        R10, BX
-	MULXQ       ·qElement+16(SB), AX, R10
-	ADCQ        AX, SI
-	ADCQ        R10, DI
-	ADCQ        $0, R8
-	MULXQ       ·qElement+8(SB), AX, R10
-	ADDQ        AX, BX
-	ADCQ        R10, SI
-	MULXQ       ·qElement+24(SB), AX, R10
-	ADCQ        AX, DI
-	ADCQ        R10, R8
-	ADCQ        $0, R9
-	VMOVQ       X0, AX
-	ADDQ        AX, BX
-	VALIGNQ     $1, Z0, Z0, Z0
-	VMOVQ       X0, AX
-	ADCQ        AX, SI
-	VALIGNQ     $1, Z0, Z0, Z0
-	VMOVQ       X0, AX
-	ADCQ        AX, DI
-	VALIGNQ     $1, Z0, Z0, Z0
-	VMOVQ       X0, AX
-	ADCQ        AX, R8
-	VALIGNQ     $1, Z0, Z0, Z0
-	VMOVQ       X0, AX
-	ADCQ        AX, R9
-	MOVQ        R8, AX
-	SHRQ        $32, R9, AX
-	MOVQ        $const_mu, DX
-	MULQ        DX
-	MULXQ       ·qElement+0(SB), AX, R10
-	SUBQ        AX, BX
-	SBBQ        R10, SI
-	MULXQ       ·qElement+16(SB), AX, R10
-	SBBQ        AX, DI
-	SBBQ        R10, R8
-	SBBQ        $0, R9
-	MULXQ       ·qElement+8(SB), AX, R10
-	SUBQ        AX, SI
-	SBBQ        R10, DI
-	MULXQ       ·qElement+24(SB), AX, R10
-	SBBQ        AX, R8
-	SBBQ        R10, R9
-	MOVQ        res+0(FP), R11
-	MOVQ        BX, 0(R11)
-	MOVQ        SI, 8(R11)
-	MOVQ        DI, 16(R11)
-	MOVQ        R8, 24(R11)
-	SUBQ        ·qElement+0(SB), BX
-	SBBQ        ·qElement+8(SB), SI
-	SBBQ        ·qElement+16(SB), DI
-	SBBQ        ·qElement+24(SB), R8
-	SBBQ        $0, R9
-	JCS         done_14
-	MOVQ        BX, 0(R11)
-	MOVQ        SI, 8(R11)
-	MOVQ        DI, 16(R11)
-	MOVQ        R8, 24(R11)
-	SUBQ        ·qElement+0(SB), BX
-	SBBQ        ·qElement+8(SB), SI
-	SBBQ        ·qElement+16(SB), DI
-	SBBQ        ·qElement+24(SB), R8
-	SBBQ        $0, R9
-	JCS         done_14
-	MOVQ        BX, 0(R11)
-	MOVQ        SI, 8(R11)
-	MOVQ        DI, 16(R11)
-	MOVQ        R8, 24(R11)
+
+	// Extract the 4 least significant qwords of Z0
+	VMOVQ   X0, SI
+	VALIGNQ $1, Z0, Z1, Z0
+	VMOVQ   X0, DI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R8
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, R9
+	VALIGNQ $1, Z0, Z0, Z0
+	XORQ    BX, BX
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   SI, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, SI
+	ADCQ    R10, DI
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, R8
+	ADCQ    R10, R9
+	ADCQ    $0, BX
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, DI
+	ADCQ    R10, R8
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, R9
+	ADCQ    R10, BX
+	ADCQ    $0, SI
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   DI, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, DI
+	ADCQ    R10, R8
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, R9
+	ADCQ    R10, BX
+	ADCQ    $0, SI
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, R8
+	ADCQ    R10, R9
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, BX
+	ADCQ    R10, SI
+	ADCQ    $0, DI
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   R8, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, R8
+	ADCQ    R10, R9
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, BX
+	ADCQ    R10, SI
+	ADCQ    $0, DI
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, R9
+	ADCQ    R10, BX
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, SI
+	ADCQ    R10, DI
+	ADCQ    $0, R8
+	MOVQ    $const_qInvNeg, DX
+	MULXQ   R9, DX, R10
+	MULXQ   ·qElement+0(SB), AX, R10
+	ADDQ    AX, R9
+	ADCQ    R10, BX
+	MULXQ   ·qElement+16(SB), AX, R10
+	ADCQ    AX, SI
+	ADCQ    R10, DI
+	ADCQ    $0, R8
+	MULXQ   ·qElement+8(SB), AX, R10
+	ADDQ    AX, BX
+	ADCQ    R10, SI
+	MULXQ   ·qElement+24(SB), AX, R10
+	ADCQ    AX, DI
+	ADCQ    R10, R8
+	ADCQ    $0, R9
+	VMOVQ   X0, AX
+	ADDQ    AX, BX
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, SI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, DI
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, R8
+	VALIGNQ $1, Z0, Z0, Z0
+	VMOVQ   X0, AX
+	ADCQ    AX, R9
+
+	// Barrett reduction; see Handbook of Applied Cryptography, Algorithm 14.42.
+	MOVQ  R8, AX
+	SHRQ  $32, R9, AX
+	MOVQ  $const_mu, DX
+	MULQ  DX
+	MULXQ ·qElement+0(SB), AX, R10
+	SUBQ  AX, BX
+	SBBQ  R10, SI
+	MULXQ ·qElement+16(SB), AX, R10
+	SBBQ  AX, DI
+	SBBQ  R10, R8
+	SBBQ  $0, R9
+	MULXQ ·qElement+8(SB), AX, R10
+	SUBQ  AX, SI
+	SBBQ  R10, DI
+	MULXQ ·qElement+24(SB), AX, R10
+	SBBQ  AX, R8
+	SBBQ  R10, R9
+
+	// we need up to 2 conditional substractions to be < q
+	MOVQ res+0(FP), R11
+	MOVQ BX, 0(R11)
+	MOVQ SI, 8(R11)
+	MOVQ DI, 16(R11)
+	MOVQ R8, 24(R11)
+	SUBQ ·qElement+0(SB), BX
+	SBBQ ·qElement+8(SB), SI
+	SBBQ ·qElement+16(SB), DI
+	SBBQ ·qElement+24(SB), R8
+	SBBQ $0, R9
+	JCS  done_14
+	MOVQ BX, 0(R11)
+	MOVQ SI, 8(R11)
+	MOVQ DI, 16(R11)
+	MOVQ R8, 24(R11)
+	SUBQ ·qElement+0(SB), BX
+	SBBQ ·qElement+8(SB), SI
+	SBBQ ·qElement+16(SB), DI
+	SBBQ ·qElement+24(SB), R8
+	SBBQ $0, R9
+	JCS  done_14
+	MOVQ BX, 0(R11)
+	MOVQ SI, 8(R11)
+	MOVQ DI, 16(R11)
+	MOVQ R8, 24(R11)
 
 done_14:
 	RET
diff --git a/field/generator/asm/amd64/build.go b/field/generator/asm/amd64/build.go
index 0625f6216..2ed95e40d 100644
--- a/field/generator/asm/amd64/build.go
+++ b/field/generator/asm/amd64/build.go
@@ -23,8 +23,6 @@ import (
 	"path/filepath"
 	"strings"
 
-	"github.com/consensys/bavard"
-
 	"github.com/consensys/bavard/amd64"
 	"github.com/consensys/gnark-crypto/field/generator/config"
 )
@@ -78,6 +76,35 @@ func (f *FFAmd64) StackSize(maxNbRegistersNeeded, nbRegistersReserved, minStackS
 	return max(r, minStackSize)
 }
 
+func (f *FFAmd64) Define(name string, nbInputs int, fn func(args ...amd64.Register)) func(args ...amd64.Register) {
+
+	inputs := make([]string, nbInputs)
+	for i := 0; i < nbInputs; i++ {
+		inputs[i] = fmt.Sprintf("in%d", i)
+	}
+	name = strings.ToUpper(name)
+	f.StartDefine()
+	f.WriteLn("#define " + name + "(" + strings.Join(inputs, ", ") + ")")
+	inputsRegisters := make([]amd64.Register, nbInputs)
+	for i := 0; i < nbInputs; i++ {
+		inputsRegisters[i] = amd64.Register(inputs[i])
+	}
+	fn(inputsRegisters...)
+	f.EndDefine()
+	f.WriteLn("")
+
+	return func(args ...amd64.Register) {
+		if len(args) != nbInputs {
+			panic("invalid number of arguments")
+		}
+		inputsStr := make([]string, len(args))
+		for i := 0; i < len(args); i++ {
+			inputsStr[i] = string(args[i])
+		}
+		f.WriteLn(name + "(" + strings.Join(inputsStr, ", ") + ")")
+	}
+}
+
 func max(a, b int) int {
 	if a > b {
 		return a
@@ -214,7 +241,7 @@ func GenerateFieldWrapper(w io.Writer, F *config.FieldConfig, asmDirBuildPath, a
 // see internal/templates/ops*
 func GenerateCommonASM(w io.Writer, nbWords int) error {
 	f := NewFFAmd64(w, nbWords)
-	f.WriteLn(bavard.Apache2Header("ConsenSys Software Inc.", 2020))
+	f.Comment("Code generated by gnark-crypto/generator. DO NOT EDIT.")
 
 	f.WriteLn("#include \"textflag.h\"")
 	f.WriteLn("#include \"funcdata.h\"")
@@ -246,6 +273,9 @@ func GenerateCommonASM(w io.Writer, nbWords int) error {
 func GenerateVectorASM(w io.Writer, nbWords int) error {
 	f := NewFFAmd64(w, nbWords)
 	f.WriteLn("")
+	f.Comment("Code generated by gnark-crypto/generator. DO NOT EDIT.")
+	f.Comment("Functions are derived from Dag Arne Osvik's work in github.com/a16z/vectorized-fields")
+	f.WriteLn("")
 
 	f.generateAddVec()
 	f.generateSubVec()
diff --git a/field/generator/asm/amd64/element_mul.go b/field/generator/asm/amd64/element_mul.go
index b5791bc30..c7c17af53 100644
--- a/field/generator/asm/amd64/element_mul.go
+++ b/field/generator/asm/amd64/element_mul.go
@@ -110,6 +110,7 @@ func (f *FFAmd64) MulADX(registers *amd64.Registers, x, y func(int) string, t []
 		if !hasFreeRegister {
 			f.POPQ(A)
 		}
+
 		// for j=1 to N-1
 		//    (C,t[j-1]) := t[j] + m*q[j] + C
 		for j := 1; j < f.NbWords; j++ {
diff --git a/field/generator/asm/amd64/element_vec.go b/field/generator/asm/amd64/element_vec.go
index 415208b8b..1a5350b23 100644
--- a/field/generator/asm/amd64/element_vec.go
+++ b/field/generator/asm/amd64/element_vec.go
@@ -16,7 +16,6 @@ package amd64
 
 import (
 	"fmt"
-	"strconv"
 
 	"github.com/consensys/bavard/amd64"
 )
@@ -427,15 +426,17 @@ func (f *FFAmd64) generateSumVec() {
 		hi, lo amd64.Register
 	}
 
-	f.WriteLn(`#define SPLIT_LO_HI(lo, hi) \
-		MOVQ hi, lo; \
-		ANDQ $0xffffffff, lo; \
-		SHLQ $32, lo; \
-		SHRQ $32, hi; \
-	`)
+	splitLoHi := f.Define("SPLIT_LO_HI", 2, func(args ...amd64.Register) {
+		lo := args[0]
+		hi := args[1]
+		f.MOVQ(hi, lo)
+		f.ANDQ("$0xffffffff", lo)
+		f.SHLQ("$32", lo)
+		f.SHRQ("$32", hi)
+	})
 
 	for _, v := range []hilo{{w0h, low0h}, {w1h, low1h}, {w2h, low2h}, {w3h, low3h}} {
-		f.WriteLn(`SPLIT_LO_HI(` + string(v.lo) + `, ` + string(v.hi) + `)`)
+		splitLoHi(v.lo, v.hi)
 	}
 
 	f.WriteLn(`
@@ -579,15 +580,12 @@ func (f *FFAmd64) generateInnerProduct() {
 	A6H := amd64.Register("Z30")
 	A7H := amd64.Register("Z31")
 
-	// X0 := amd64.Register("X0")
-
 	// load arguments
 	f.MOVQ("a+8(FP)", PX)
 	f.MOVQ("b+16(FP)", PY)
 	f.MOVQ("n+24(FP)", LEN)
 
-	// Create mask for low dword in each qword
-	// vpmovzxdq	%ymm0, LSW
+	f.Comment("Create mask for low dword in each qword")
 	f.VPCMPEQB("Y0", "Y0", "Y0")
 	f.VPMOVZXDQ("Y0", LSW)
 
@@ -623,53 +621,26 @@ func (f *FFAmd64) generateInnerProduct() {
 
 	f.Comment("we multiply and accumulate partial products of 4 bytes * 32 bytes")
 
-	f.VPMULUDQ_BCST("0*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A0L, A0L)
-	f.VPADDQ(PPH, A0H, A0H)
-
-	f.VPMULUDQ_BCST("1*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A1L, A1L)
-	f.VPADDQ(PPH, A1H, A1H)
-
-	f.VPMULUDQ_BCST("2*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A2L, A2L)
-	f.VPADDQ(PPH, A2H, A2H)
-
-	f.VPMULUDQ_BCST("3*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A3L, A3L)
-	f.VPADDQ(PPH, A3H, A3H)
-
-	f.VPMULUDQ_BCST("4*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A4L, A4L)
-	f.VPADDQ(PPH, A4H, A4H)
-
-	f.VPMULUDQ_BCST("5*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A5L, A5L)
-	f.VPADDQ(PPH, A5H, A5H)
-
-	f.VPMULUDQ_BCST("6*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A6L, A6L)
-	f.VPADDQ(PPH, A6H, A6H)
-
-	f.VPMULUDQ_BCST("7*4("+PX+")", Y, PPL)
-	f.VPSRLQ("$32", PPL, PPH)
-	f.VPANDQ(LSW, PPL, PPL)
-	f.VPADDQ(PPL, A7L, A7L)
-	f.VPADDQ(PPH, A7H, A7H)
+	mac := f.Define("MAC", 3, func(inputs ...amd64.Register) {
+		opLeft := inputs[0]
+		lo := inputs[1]
+		hi := inputs[2]
+
+		f.VPMULUDQ_BCST(opLeft, Y, PPL)
+		f.VPSRLQ("$32", PPL, PPH)
+		f.VPANDQ(LSW, PPL, PPL)
+		f.VPADDQ(PPL, lo, lo)
+		f.VPADDQ(PPH, hi, hi)
+	})
+
+	mac("0*4("+PX+")", A0L, A0H)
+	mac("1*4("+PX+")", A1L, A1H)
+	mac("2*4("+PX+")", A2L, A2H)
+	mac("3*4("+PX+")", A3L, A3H)
+	mac("4*4("+PX+")", A4L, A4H)
+	mac("5*4("+PX+")", A5L, A5H)
+	mac("6*4("+PX+")", A6L, A6H)
+	mac("7*4("+PX+")", A7L, A7H)
 
 	f.ADDQ("$32", PX)
 
@@ -679,6 +650,7 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.Push(&registers, LEN, PX, PY)
 
 	f.LABEL(AddPP)
+	f.Comment("we accumulate the partial products into 544bits in Z1:Z0")
 
 	f.MOVQ(uint64(0x1555), amd64.AX)
 	f.KMOVD(amd64.AX, "K1")
@@ -706,7 +678,13 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.VALIGND("$15", ACC, ACC, "K2", "Z0")
 	f.KSHIFTLW("$1", "K2", "K2")
 
-	ADDPP := func(AxH, AyL, AyH, AzL, I amd64.Register) {
+	f.Comment("macro to add partial products and store the result in Z0")
+	addPP := f.Define("ADDPP", 5, func(inputs ...amd64.Register) {
+		AxH := inputs[0]
+		AyL := inputs[1]
+		AyH := inputs[2]
+		AzL := inputs[3]
+		I := inputs[4]
 		f.VPSRLQ("$32", ACC, PPL)
 		f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
 		f.VPADDQ(PPL, ACC, ACC)
@@ -720,14 +698,14 @@ func (f *FFAmd64) generateInnerProduct() {
 		f.VPADDQ(PPL, ACC, ACC)
 		f.VALIGND("$16-"+I, ACC, ACC, "K2", "Z0")
 		f.KADDW("K2", "K2", "K2")
-	}
+	})
 
-	ADDPP(A0H, A1L, A1H, A2L, "2")
-	ADDPP(A1H, A2L, A2H, A3L, "3")
-	ADDPP(A2H, A3L, A3H, A4L, "4")
-	ADDPP(A3H, A4L, A4H, A5L, "5")
-	ADDPP(A4H, A5L, A5H, A6L, "6")
-	ADDPP(A5H, A6L, A6H, A7L, "7")
+	addPP(A0H, A1L, A1H, A2L, "2")
+	addPP(A1H, A2L, A2H, A3L, "3")
+	addPP(A2H, A3L, A3H, A4L, "4")
+	addPP(A3H, A4L, A4H, A5L, "5")
+	addPP(A4H, A5L, A5H, A6L, "6")
+	addPP(A5H, A6L, A6H, A7L, "7")
 
 	f.VPSRLQ("$32", ACC, PPL)
 	f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
@@ -749,20 +727,20 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.VALIGND("$16-9", ACC, ACC, "K2", "Z0")
 	f.KSHIFTLW("$1", "K2", "K2")
 
-	ADDPP_2 := func(I int) {
+	addPP2 := f.Define("ADDPP2", 1, func(args ...amd64.Register) {
 		f.VPSRLQ("$32", ACC, PPL)
 		f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
 		f.VPADDQ(PPL, ACC, ACC)
-		f.VALIGND("$16-"+strconv.Itoa(I), ACC, ACC, "K2", "Z0")
+		f.VALIGND("$16-"+args[0], ACC, ACC, "K2", "Z0")
 		f.KSHIFTLW("$1", "K2", "K2")
-	}
+	})
 
-	ADDPP_2(10)
-	ADDPP_2(11)
-	ADDPP_2(12)
-	ADDPP_2(13)
-	ADDPP_2(14)
-	ADDPP_2(15)
+	addPP2("10")
+	addPP2("11")
+	addPP2("12")
+	addPP2("13")
+	addPP2("14")
+	addPP2("15")
 
 	f.VPSRLQ("$32", ACC, PPL)
 	f.VALIGND_Z("$2", ACC, ACC, "K1", ACC)
@@ -775,14 +753,7 @@ func (f *FFAmd64) generateInnerProduct() {
 	T3 := f.Pop(&registers)
 	T4 := f.Pop(&registers)
 
-	// Extract the 4 least significant qwords of %zmm0
-
-	// vmovq	%xmm0, T1; valignq	$1, %zmm0, %zmm1, %zmm0	// Shift in low word from zmm1
-	// vmovq	%xmm0, T2; valignq	$1, %zmm0, %zmm0, %zmm0
-	// vmovq	%xmm0, T3; valignq	$1, %zmm0, %zmm0, %zmm0
-	// vmovq	%xmm0, T4; valignq	$1, %zmm0, %zmm0, %zmm0
-	// xorq	T0, T0
-
+	f.Comment("Extract the 4 least significant qwords of Z0")
 	f.VMOVQ("X0", T1)
 	f.VALIGNQ("$1", "Z0", "Z1", "Z0")
 	f.VMOVQ("X0", T2)
@@ -793,14 +764,6 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
 	f.XORQ(T0, T0)
 
-	// movq	INV, %rdx	// Load negative inverse mod 2^64
-
-	// mulx	T1, %rdx, PH
-
-	// mulx	0*8(PM), PL, PH; add	PL, T1; adc	PH, T2
-	// mulx	2*8(PM), PL, PH; adc	PL, T3; adc	PH, T4; adc	$0, T0
-	// mulx	1*8(PM), PL, PH; add	PL, T2; adc	PH, T3
-	// mulx	3*8(PM), PL, PH; adc	PL, T4; adc	PH, T0; adc	$0, T1
 	PH := f.Pop(&registers)
 	PL := amd64.AX
 	f.MOVQ(f.qInv0(), amd64.DX)
@@ -820,15 +783,6 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.ADCQ(PH, T0)
 	f.ADCQ("$0", T1)
 
-	// // movq	INV, %rdx
-
-	// // mulx	T2, %rdx, PH
-
-	// // mulx	0*8(PM), PL, PH; add	PL, T2; adc	PH, T3
-	// // mulx	2*8(PM), PL, PH; adc	PL, T4; adc	PH, T0; adc	$0, T1
-	// // mulx	1*8(PM), PL, PH; add	PL, T3; adc	PH, T4
-	// // mulx	3*8(PM), PL, PH; adc	PL, T0; adc	PH, T1; adc	$0, T2
-
 	f.MOVQ(f.qInv0(), amd64.DX)
 	f.MULXQ(T2, amd64.DX, PH)
 
@@ -847,15 +801,6 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.ADCQ(PH, T1)
 	f.ADCQ("$0", T2)
 
-	// // movq	INV, %rdx
-
-	// // mulx	T3, %rdx, PH
-
-	// // mulx	0*8(PM), PL, PH; add	PL, T3; adc	PH, T4
-	// // mulx	2*8(PM), PL, PH; adc	PL, T0; adc	PH, T1; adc	$0, T2
-	// // mulx	1*8(PM), PL, PH; add	PL, T4; adc	PH, T0
-	// // mulx	3*8(PM), PL, PH; adc	PL, T1; adc	PH, T2; adc	$0, T3
-
 	f.MOVQ(f.qInv0(), amd64.DX)
 
 	f.MULXQ(T3, amd64.DX, PH)
@@ -875,15 +820,6 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.ADCQ(PH, T2)
 	f.ADCQ("$0", T3)
 
-	// // movq	INV, %rdx
-
-	// // mulx	T4, %rdx, PH
-
-	// // mulx	0*8(PM), PL, PH; add	PL, T4; adc	PH, T0
-	// // mulx	2*8(PM), PL, PH; adc	PL, T1; adc	PH, T2; adc	$0, T3
-	// // mulx	1*8(PM), PL, PH; add	PL, T0; adc	PH, T1
-	// // mulx	3*8(PM), PL, PH; adc	PL, T2; adc	PH, T3; adc	$0, T4
-
 	f.MOVQ(f.qInv0(), amd64.DX)
 
 	f.MULXQ(T4, amd64.DX, PH)
@@ -905,12 +841,6 @@ func (f *FFAmd64) generateInnerProduct() {
 
 	// Add the remaining 5 qwords (9 dwords) from zmm0
 
-	// vmovq	%xmm0, PL; add	PL, T0;	valignq	$1, %zmm0, %zmm0, %zmm0
-	// vmovq	%xmm0, PL; adc	PL, T1;	valignq	$1, %zmm0, %zmm0, %zmm0
-	// vmovq	%xmm0, PL; adc	PL, T2;	valignq	$1, %zmm0, %zmm0, %zmm0
-	// vmovq	%xmm0, PL; adc	PL, T3;	valignq	$1, %zmm0, %zmm0, %zmm0
-	// vmovq	%xmm0, PL; adc	PL, T4	// T4 < 2^32
-
 	f.VMOVQ("X0", PL)
 	f.ADDQ(PL, T0)
 	f.VALIGNQ("$1", "Z0", "Z0", "Z0")
@@ -926,31 +856,12 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.VMOVQ("X0", PL)
 	f.ADCQ(PL, T4)
 
-	//////////////////////////////////////////////////
-	// Barrett reduction
-	//////////////////////////////////////////////////
-
-	// // For explanation of mu, q1, q2, q3, r1, r2, see Handbook of
-	// // Applied Cryptography, Algorithm 14.42.
-
-	// // q1 is low 32 bits of T4 and high 32 bits of T3
-
-	// movq	T3, %rax
-	// shrd	$32, T4, %rax	// q1
-	// mulq	MU		// Multiply by mu. q2 in rdx:rax, q3 in rdx
-
+	f.Comment("Barrett reduction; see Handbook of Applied Cryptography, Algorithm 14.42.")
 	f.MOVQ(T3, amd64.AX)
 	f.SHRQw("$32", T4, amd64.AX)
 	f.MOVQ(f.mu(), amd64.DX)
 	f.MULQ(amd64.DX)
 
-	// // Subtract r2 from r1
-
-	// mulx	0*8(PM), PL, PH; sub	PL, T0; sbb	PH, T1;
-	// mulx	2*8(PM), PL, PH; sbb	PL, T2; sbb	PH, T3;	sbb	$0, T4
-	// mulx	1*8(PM), PL, PH; sub	PL, T1; sbb	PH, T2;
-	// mulx	3*8(PM), PL, PH; sbb	PL, T3; sbb	PH, T4
-
 	f.MULXQ(f.qAt(0), PL, PH)
 	f.SUBQ(PL, T0)
 	f.SBBQ(PH, T1)
@@ -965,6 +876,8 @@ func (f *FFAmd64) generateInnerProduct() {
 	f.SBBQ(PL, T3)
 	f.SBBQ(PH, T4)
 
+	f.Comment("we need up to 2 conditional substractions to be < q")
+
 	PZ := f.Pop(&registers)
 	f.MOVQ("res+0(FP)", PZ)
 	t := []amd64.Register{T0, T1, T2, T3}
@@ -996,140 +909,4 @@ func (f *FFAmd64) generateInnerProduct() {
 
 	f.RET()
 
-	// f.Push(&registers, lo, hi)
-
-	// // We have 544-bit (72-byte) result in Z1:Z0.
-	// // Only the modular reduction remains to be computed.
-
-	// // for i=0 to s-1
-	// // 	C := 0
-	// // 	m := t[i]*n'[0] mod W
-	// // 	for j=0 to s-1
-	// // 		(C,S) := t[i+j] + m*n[j] + C
-	// // 		t[i+j] := S
-	// // 	ADD (t[i+s],C)
-
-	// f.XORQ(amd64.AX, amd64.AX)
-	// m := amd64.DX
-	// tr := f.Pop(&registers)
-	// zero := f.Pop(&registers)
-
-	// f.MOVQ(f.qInv0(), m)
-	// for i := 0; i < 4; i++ {
-	// 	f.XORQ(zero, zero)
-	// 	f.IMULQ(r[i], m)
-
-	// 	f.MULXQ(f.qAt(i), amd64.AX, tr)
-
-	// 	// shift in the loop.
-
-	// 	for j := 0; j < 4; j++ {
-	// 		f.MULXQ(f.qAt(j), amd64.AX, tr)
-	// 		f.ADCXQ(amd64.AX, r[i+j])
-	// 		f.ADOXQ(tr, r[i+j+1])
-	// 	}
-
-	// 	for j := i + 1; j < 8; j++ {
-	// 		f.ADCXQ(zero, r[j])
-	// 		f.ADOXQ(zero, r[j+1])
-	// 	}
-
-	// 	f.ADCXQ(zero, r[8])
-	// }
-
-	// // // j == 0
-	// // // C,_ := r[i] + m*q[0]
-	// // f.MULXQ(f.qAt(0), amd64.AX, tr)
-	// // f.ADCXQ(amd64.AX, r[i])
-	// // f.ADOXQ(tr, r[i+1])
-
-	// // for j := 1; j < 4; j++ {
-	// // 	f.MULXQ(f.qAt(j), amd64.AX, tr) // m * n[j]
-	// // 	f.ADCXQ(amd64.AX, r[i+j])
-	// // 	f.ADOXQ(tr, r[i+j+1])
-	// // }
-
-	// // for k := i + 4; k < 9; k++ {
-	// // 	f.ADCXQ(zero, r[k])
-	// // 	f.ADOXQ(zero, r[k])
-	// // }
-
-	// f.Push(&registers, zero, tr, m)
-
-	// // now our result should be in r[4] to r[8]
-	// T0 := r[4]
-	// T1 := r[5]
-	// T2 := r[6]
-	// T3 := r[7]
-	// T4 := r[8]
-
-	// PL := f.Pop(&registers)
-	// PH := f.Pop(&registers)
-
-	// // //////////////////////////////////////////////////
-	// // // Barrett reduction
-	// // //////////////////////////////////////////////////
-
-	// // // // For explanation of mu, q1, q2, q3, r1, r2, see Handbook of
-	// // // // Applied Cryptography, Algorithm 14.42.
-
-	// // // // q1 is low 32 bits of T4 and high 32 bits of T3
-
-	// // // movq	T3, %rax
-	// // // shrd	$32, T4, %rax	// q1
-	// // // mulq	MU		// Multiply by mu. q2 in rdx:rax, q3 in rdx
-
-	// f.MOVQ(T3, amd64.AX)
-	// f.SHRQw("$32", T4, amd64.AX)
-	// f.MOVQ(f.mu(), amd64.DX)
-	// f.MULQ(amd64.DX)
-
-	// // // // Subtract r2 from r1
-
-	// // // mulx	0*8(PM), PL, PH; sub	PL, T0; sbb	PH, T1;
-	// // // mulx	2*8(PM), PL, PH; sbb	PL, T2; sbb	PH, T3;	sbb	$0, T4
-	// // // mulx	1*8(PM), PL, PH; sub	PL, T1; sbb	PH, T2;
-	// // // mulx	3*8(PM), PL, PH; sbb	PL, T3; sbb	PH, T4
-
-	// f.MULXQ(f.qAt(0), PL, PH)
-	// f.SUBQ(PL, T0)
-	// f.SBBQ(PH, T1)
-	// f.MULXQ(f.qAt(2), PL, PH)
-	// f.SBBQ(PL, T2)
-	// f.SBBQ(PH, T3)
-	// f.SBBQ("$0", T4)
-	// f.MULXQ(f.qAt(1), PL, PH)
-	// f.SUBQ(PL, T1)
-	// f.SBBQ(PH, T2)
-	// f.MULXQ(f.qAt(3), PL, PH)
-	// f.SBBQ(PL, T3)
-	// f.SBBQ(PH, T4)
-
-	// PZ := f.Pop(&registers)
-	// f.MOVQ("res+0(FP)", PZ)
-	// t := []amd64.Register{T0, T1, T2, T3}
-	// f.Mov(t, PZ)
-
-	// // sub q
-	// f.SUBQ(f.qAt(0), T0)
-	// f.SBBQ(f.qAt(1), T1)
-	// f.SBBQ(f.qAt(2), T2)
-	// f.SBBQ(f.qAt(3), T3)
-	// f.SBBQ("$0", T4)
-
-	// // if borrow, we go to done
-	// f.JCS(done)
-
-	// f.Mov(t, PZ)
-
-	// f.SUBQ(f.qAt(0), T0)
-	// f.SBBQ(f.qAt(1), T1)
-	// f.SBBQ(f.qAt(2), T2)
-	// f.SBBQ(f.qAt(3), T3)
-	// f.SBBQ("$0", T4)
-
-	// f.JCS(done)
-
-	// f.Mov(t, PZ)
-
 }
diff --git a/field/generator/internal/templates/element/ops_asm.go b/field/generator/internal/templates/element/ops_asm.go
index 042337d20..df1b10671 100644
--- a/field/generator/internal/templates/element/ops_asm.go
+++ b/field/generator/internal/templates/element/ops_asm.go
@@ -86,9 +86,6 @@ func (vector *Vector) Sum() (res {{.ElementName}}) {
 //go:noescape
 func sumVec(res *{{.ElementName}}, a *{{.ElementName}}, n uint64)
 
-//go:noescape
-func innerProdVec(res *uint64, a,b *{{.ElementName}}, n uint64)
-
 // InnerProduct computes the inner product of two vectors.
 // It panics if the vectors don't have the same length.
 func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
@@ -99,10 +96,10 @@ func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
 	if n != uint64(len(other)) {
 		panic("vector.InnerProduct: vectors don't have the same length")
 	}
-	const minN = 0 // AVX512 slower than generic for small n
 	const maxN = (1 << 32) - 1
-	if !supportAvx512 || n <= minN || n >= maxN {
+	if !supportAvx512 || n >= maxN {
 		// call innerProductVecGeneric
+		// note; we could split the vector into smaller chunks and call innerProductVec
 		innerProductVecGeneric(&res, *vector, other)
 		return
 	}
@@ -111,6 +108,9 @@ func (vector *Vector) InnerProduct(other Vector) (res {{.ElementName}}) {
 	return
 }
 
+//go:noescape
+func innerProdVec(res *uint64, a,b *{{.ElementName}}, n uint64)
+
 {{- end}}
 
 // Mul z = x * y (mod q)
diff --git a/field/generator/internal/templates/element/tests_vector.go b/field/generator/internal/templates/element/tests_vector.go
index 2eb753c99..382217122 100644
--- a/field/generator/internal/templates/element/tests_vector.go
+++ b/field/generator/internal/templates/element/tests_vector.go
@@ -86,9 +86,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/field/goldilocks/vector_test.go b/field/goldilocks/vector_test.go
index 3f6711ccb..20f4f5130 100644
--- a/field/goldilocks/vector_test.go
+++ b/field/goldilocks/vector_test.go
@@ -97,9 +97,9 @@ func (vector *Vector) unmarshalBinaryAsync(data []byte) error {
 func TestVectorOps(t *testing.T) {
 	parameters := gopter.DefaultTestParameters()
 	if testing.Short() {
-		parameters.MinSuccessfulTests = 5
+		parameters.MinSuccessfulTests = 2
 	} else {
-		parameters.MinSuccessfulTests = 100
+		parameters.MinSuccessfulTests = 10
 	}
 	properties := gopter.NewProperties(parameters)
 
diff --git a/go.mod b/go.mod
index f7ed17e22..5b86c36ac 100644
--- a/go.mod
+++ b/go.mod
@@ -4,7 +4,7 @@ go 1.22
 
 require (
 	github.com/bits-and-blooms/bitset v1.14.2
-	github.com/consensys/bavard v0.0.0
+	github.com/consensys/bavard v0.1.18
 	github.com/leanovate/gopter v0.2.11
 	github.com/mmcloughlin/addchain v0.4.0
 	github.com/spf13/cobra v1.8.1
@@ -15,8 +15,6 @@ require (
 	gopkg.in/yaml.v2 v2.4.0
 )
 
-replace github.com/consensys/bavard => ../bavard
-
 require (
 	github.com/davecgh/go-spew v1.1.1 // indirect
 	github.com/inconshreveable/mousetrap v1.1.0 // indirect
diff --git a/go.sum b/go.sum
index 0f20a3a93..2e655e3e4 100644
--- a/go.sum
+++ b/go.sum
@@ -55,8 +55,8 @@ github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDk
 github.com/cncf/udpa/go v0.0.0-20191209042840-269d4d468f6f/go.mod h1:M8M6+tZqaGXZJjfX53e64911xZQV5JYwmTeXPW+k8Sc=
 github.com/cncf/udpa/go v0.0.0-20200629203442-efcf912fb354/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
 github.com/cncf/udpa/go v0.0.0-20201120205902-5459f2c99403/go.mod h1:WmhPx2Nbnhtbo57+VJT5O0JRkEi1Wbu0z5j0R8u5Hbk=
-github.com/consensys/bavard v0.1.17 h1:53CdY/g35YSH9oRoa/b29tZinaiOEJYBmf9vydozPpE=
-github.com/consensys/bavard v0.1.17/go.mod h1:9ItSMtA/dXMAiL7BG6bqW2m3NdSEObYWoH223nGHukI=
+github.com/consensys/bavard v0.1.18 h1:eYXgFO6LHm8X8BKjgKPdvOl/QXag9n54b213rsv3448=
+github.com/consensys/bavard v0.1.18/go.mod h1:k/zVjHHC4B+PQy1Pg7fgvG3ALicQw540Crag8qx+dZs=
 github.com/coreos/go-semver v0.3.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/coreos/go-systemd/v22 v22.3.2/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc=
 github.com/cpuguy83/go-md2man/v2 v2.0.0/go.mod h1:maD7wRr/U5Z6m/iR4s+kqSMx2CaBsrgA7czyZG/E6dU=